Circuits including a given set of vertices
β Scribed by Pierre Fraisse
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 180 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Let G = (V, β¬) be a digraph of order n, satisfying Woodall's condition
Let S be a subset of V of cardinality s. Then there exists a circuit including S and of length at most Min(n,2s). In the case of oriented graphs we obtain the same result under the weaker condition d'(x) + d-( y) 2 n -2 (which implies hamiltonism).
π SIMILAR VOLUMES
This note presents a solution to the following problem posed by Chen, Schelp, and SoltΓ©s: find a simple graph with the least number of vertices for which only the degrees of the vertices that appear an odd number of times are given.
This note can be treated a s a supplement to a paper written by Bollobas which was devoted to the vertices of a given degree in a random graph. We determine some values of the edge probability p for which the number of vertices of a given degree of a random graph G E ?An, p) asymptotically has a nor